Self-circularization-How to prevent other unwanted ligations

I am trying to design a protocol in which I cut a 300 DNA fragment from plasmid and circularize it, so I can have this DNA minicircle (containing 300 bp). The enzyme has 2 cut sites in the plasmid so both ends (sticky ends) are the same. When I tried to ligate it, the problem comes: There is ligation of 2, 3, 4... fragments, so I saw a ladder on the agarose gel. I am wondering if anyone has suggestions on what I should do to prevent or reduce the ligations I don't want. It will be the best for me if just have 300 bp minicircles in there.
Thank you so much.

If you do the ligation in high volume (low concentration of DNA) you will favor circularization over concatamers. 300 bp is a bit short, so the stiffness of the DNA will reduce its frequency. Can you make the strand a bit longer?

If you do the ligation in high volume (low concentration of DNA) you will favor circularization over concatamers. 300 bp is a bit short, so the stiffness of the DNA will reduce its frequency. Can you make the strand a bit longer?

Thank you so much for your reply. Unfortunately I can't make it longer. About what range of concentration would be considered 'low', please?

You can calculate this. DNA is 0.34 nm/bp long, so your 300 bp fragment will be 100 nm long. You want the probability of finding its own end to be higher than the probability of finding some other end. The local concentration of your end is 1 molecule/sphere of radius 100 nm. Volume is 4/3 pi r^3 or about 4e6 nm^3. There are (10^8)^3 nm^3/liter or 10^24 nm^3/liter. So the local concentration of ends is about 1e24/4e6 molecules/liter = .25e18 molecules/liter = .25e18 molecules/6e23 molecules/mole = .04e-5 molar = 4e-7 molar = 400 nM.

You can calculate this. DNA is 0.34 nm/bp long, so your 300 bp fragment will be 100 nm long. You want the probability of finding its own end to be higher than the probability of finding some other end. The local concentration of your end is 1 molecule/sphere of radius 100 nm. Volume is 4/3 pi r^3 or about 4e6 nm^3. There are (10^8)^3 nm^3/liter or 10^24 nm^3/liter. So the local concentration of ends is about 1e24/4e6 molecules/liter = .25e18 molecules/liter = .25e18 molecules/6e23 molecules/mole = .04e-5 molar = 4e-7 molar = 400 nM.

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